Question

You are retiring and you have $300000 save in your retirement account today. The account earns interest at an annual rate of 12%. You are considering several alternatives for your payments. Determine the payment amount under each of the following circumstances:

a) Your payments are received annually for the next 20 years and interest is compounded annually:

b) Your payments are received semi- annually for the next 20 years and interest is compounded semi- annually:

c) Your payments are received quarterly for the next 20 years and interest is compounded quarterly:

d) which alternative would you choose and why?

Answer 1

a) No of periods = 20

Rate per period = 12%

PV = $300000

Using PMT function in excel:

Annual Payment =PMT(12%,20,-300000,0) = $40,163.63

b) No of periods = 20*2 = 40

Rate per period = 12%/2 = 6%

PV = $300000

Using PMT function in excel:

Semi-Annual Payment =PMT(6%,40,-300000,0) = $19,938.46

c) No of periods = 20*4 = 80 Rate per period = 12%/4 = 3% PV = $300000 Using PMT function in excel: QuaterlyPayment =PMT(3%,80,-300000,0)   =$9,933.52 d) Alternative a should be choosen as the interest received in this case is the highest. Interest = Total of all payments - Principal Interest in Alternative A = $503,272.68 Interest in Alternative B = $497,538.43 Interest in Alternative C = $494,681.90